The "evidential" paradigm is a statistical paradigm, an alternative to frequentist and Bayesian paradigms for statistical inference. The evidential paradigm provides 4 major advantages over these other paradigms when analyzing genetic data: It (1) provides an objective measure of evidence;(2) has good operating characteristics (low error probabilities);(3) decouples the error probabilities from the measure of evidence;and - perhaps the advantage with the greatest potential impact - (4) provides better approaches to deal with the multiple testing problem. In Strug &Hodge (2006a, b) we quantified these advantages for linkage analysis of several simple genetic models, mostly with known parameters. Here we propose to extend our investigations to more complex genetic models, also with unknown parameters, and to association analysis: Specifically, we will (1) Extend linkage findings to association analysis, including genome-wide association studies;(2) Quantify error probabilities for linkage of more complex disease models;and (3) Develop and test new evidential methodology for linkage analysis of complex unknown traits. We will test and characterize new methods via rigorous theoretical analyses, supplemented by realistic computer simulations. /Relevance The long-term objective is to make the evidential paradigm, with its multiple testing advantages, available for use when analyzing all types of genetic data. As a result, some current problems imposed by conducting multiple tests on genetic data, for example, investigators'reluctance to thoroughly analyze their collected data, will no longer bedevil the field or stunt the advancement of knowledge.